I cannot be first person to think of this idea: drill hole in rake-head and slide a naturally-grown handle to just fit. There are no stays or bows to fix it.Here are 2 prototype ash heads with willow handles. One is fixed with a wedge, and one just rammed on.

To much sideways presure on a central handle, and useing willow for a handle, this wood easily compresess which will make the head loose quicker.In this area willow is used for the head and ash for handles, split rather than bowsRichard

Looks like it should work, that's how brush heads are often fitted to brushes. If you dried the handle & used a greener piece of wood for the head, the fit should tighten as the head dries (the same technique used in chair/stool/shave-horse making). You could always tap a nail/"brad" through too, to help prevent the head from being accidentally knocked loose.

Perhaps the advantage of side stays is that you can use a shallower (& therefore smaller & lighter) piece of wood for the head? But you'd still need some depth to support the tines (which will be at 90 degrees to the handle), so perhaps not. Alternatively, perhaps your joint will work loose quicker with use/wear? Aesthetics: side-stays look good .